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Run fault codes check as it may be a failed cam/crank position sensor that will not allow it to start or some other faulty sensor that is the problem. Do not waste money until you know what you have to replace

This intermittent kind of "no start" problem can often be a result of a failing anti theft system. Read this link and compare you symptoms. If you see a light that reads "security" when this happens, then this is definitely your problem.
http://vatspasslockpasskeysecurityhelp.yolasite.com/

How did you determine that the sensor failed. Did the check engine light come on? When you say that the fan won't turn, do you mean that it won't turn on and run or that you can't physically turn it by hand. To determine this, disconnect the electrical connector to the fan and try to turn it by hand. It should turn easily. If it doesn't then it must be replaced. If it does then reconnect the electrical connector to the fan and try to operate it by disconnecting the temperature sensor lead and placing a jumper wire between the terminals of the harness. turn the AC control to AC/MAX and turn the ignition key to on. If the fan runs then the problem is the sensor. If it doesn't then check the fan control relay and any related fuses. WARNING : Use extreme caution when testing the fan circuit. Never attempt to turn the fan with the electrical connector in place. The fan can operate at any time even if the engine is off.

this could be a poor battery,that the cold temperatures affect its ability to function at colder temperatures.you don`t say if it doesn`t start (fire up) or it doesn`t start(turn over)either way have the battery load tested or if its over say 7 years replace.